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Question

# Sixteen players S1,S2,...,S16 play in a tournament. They are divided into eight pairs at random. From each pair a winner is decided on the basis of a game played between the two players of the pair. Assuming that all the players are to equal strength. The probability that the players S1 is among the eight winners is

A
12
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B
13
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C
23
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D
None of these
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Solution

## The correct option is A 12Since all players are of equal strength, with whom S1 is paired, will have no bearing on the probability of his winning.The number of ways of choosing 8 winners out of 16 is 16C8The number of ways of choosing S1 and 7 other winners out of 15 is 15C7∴ Probability that S1 will win =15C716C8=15!7!8!8!8!16!=12

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